President Shimon Peres gave Mr Netanyahu another two weeks, saying democracy takes effort.
His Likud-Beitenu alliance emerged as the biggest bloc in January's vote, but with a sharply reduced number of seats.
Mr Netanyahu has been unable to make a deal with potential coalition partners.
After the meeting with Mr Peres on Saturday, Mr Netanyahu said that some parties were boycotting others.
The centrist Yesh Atid party and the right-wing Habayit Hayehudi (Jewish Home) are refusing to enter a coalition with ultra-Orthodox parties, who oppose their efforts to end military draft exemptions for students at religious seminaries.
The talks began after Israel's right-wing and centre-left blocs each secured 60 seats in the 120-member parliament (Knesset).